How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=20, b=21, c=29?

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How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=20, b=21, c=29?

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Answer 1 · 2018-02-23T19:01:16

$cos B = \frac{a}{c} = \frac{21}{29}$ $cosB=a/c=21/29$

$sin B = \frac{b}{c} = \frac{20}{29}$ $sinB=b/c=20/29$

$tan B = \frac{b}{a} = \frac{20}{21}$ $tanB=b/a=20/21$

$cot B = \frac{a}{b} = \frac{21}{20}$ $cotB=a/b=21/20$

$sec B = \frac{c}{a} = \frac{29}{21}$ $secB=c/a=29/21$

$csc B = \frac{c}{b} = \frac{29}{20}$ $cscB=c/b=29/20$

Explanation:

Verification:

$20^{2} = 400$ $20^2=400$
$21^{2} = 441$ $21^2=441$
$20^{2} + 21^{2} = 400 + 441$ $20^2+21^2=400+441$
$20^{2} + 21^{2} = 841$ $20^2+21^2=841$
$29^{2} = 841$ $29^2=841$
It is confirmed that the triangle is a right angled triangle
$a = 20$ $a=20$
$b = 21$ $b=21$
$c = 29$ $c=29$
$C = 90^{\circ}$ $C=90^@$
Thus with c=29 being considered as hypotenuse
Consider a=21 to form the adjacent side
, and b=20 to form the opposite side
the angle under consideration is B

Now,

$cos B = \frac{a}{c} = \frac{21}{29}$ $cosB=a/c=21/29$

$sin B = \frac{b}{c} = \frac{20}{29}$ $sinB=b/c=20/29$

$tan B = \frac{b}{a} = \frac{20}{21}$ $tanB=b/a=20/21$

$cot B = \frac{a}{b} = \frac{21}{20}$ $cotB=a/b=21/20$

$sec B = \frac{c}{a} = \frac{29}{21}$ $secB=c/a=29/21$

$csc B = \frac{c}{b} = \frac{29}{20}$ $cscB=c/b=29/20$

Answer 2 · 2018-02-23T19:04:08

all trignometric functions of right triangle, AC= hypotenuse=c
BC=a and AC= b are adjacent or opposite sides in accordance to the acute angles, either A or B

Explanation:

if we take angle A as the acute angle,
$sin A = \frac{a}{c} = \frac{20}{29} = \frac{o p p}{h y p}$ $sinA= a/c=20/29=(opp)/(hyp)$
$cos A = \frac{b}{c} = \frac{21}{29} = \frac{a d j}{h y p}$ $cosA=b/c=21/29=(adj)/(hyp)$
$sec A = \frac{c}{b} = \frac{29}{21} = \frac{h y p}{a d j}$ $secA=c/b=29/21=(hyp)/(adj)$
$cos e c A = \frac{c}{a} = \frac{29}{20} = \frac{h y p}{o p p}$ $cosecA=c/a=29/20=(hyp)/(opp)$
$tan A = \frac{a}{b} = \frac{20}{21} = \frac{o p p}{a d j}$ $tanA=a/b=20/21=(opp)/(adj)$
$cot A = \frac{b}{a} = \frac{21}{20} = \frac{a d j}{o p p}$ $cotA= b/a=21/20=(adj)/(opp)$
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if we take angle B as the acute angle,
$sin B = \frac{b}{c} = \frac{21}{29} = \frac{o p p}{h y p}$ $sinB= b/c=21/29=(opp)/(hyp)$
$cos B = \frac{a}{c} = \frac{20}{29} = \frac{a d j}{h y p}$ $cosB=a/c=20/29=(adj)/(hyp)$
$sec B = \frac{c}{a} = \frac{29}{20} = \frac{h y p}{a d j}$ $secB=c/a=29/20=(hyp)/(adj)$
$cos e c B = \frac{c}{b} = \frac{29}{21} = \frac{h y p}{o p p}$ $cosecB=c/b=29/21=(hyp)/(opp)$
$tan B = \frac{b}{a} = \frac{21}{20} = \frac{o p p}{a d j}$ $tanB=b/a=21/20=(opp)/(adj)$
$cot B = \frac{a}{b} = \frac{20}{21} = \frac{a d j}{o p p}$ $cotB= a/b=20/21=(adj)/(opp)$

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How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=20, b=21, c=29?

2 Answers

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